Analysis Of Rayleigh-benard Convenction Based On POD Low Dimension Modeling

Flow control and structural optimization are common problems in actual industrial design,for these problems demand the calculation result of velocity field in a short time,the traditional numerical methods is very hard to implement.The low dimension model(LDM)of flow proposed in recent years can obtain the calculation result in a short period of time,so it is an ideal numerical method for the calculation of flow control and structural optimization.It is of great significance to develop the LDM for turbulent flow.The low dimensional model(LDM)is a method to reduce the degree of freedom of the system,which can greatly reduce the computation time.The main idea of it is to analyze the flow process and extract the dominant flow modes.Then the flow process can be rewritten as the linear superposition of these basis functions.The energy spectrum of POD(Proper orthogonal decomposition)basis function has the fastest convergence speed than any other orthogonal basis(Fourier basis,Taylor basis et.al),therefore,using POD basis function to developing the LDM Will reduce the computation time as far as possible.Most of the present study about POD LDM are focus on flow or heat transfer problems individually and just a few researches pay attention to thermal fluid problems,besides,there are very little researches about the application of POD LDM to flow of NonNewtonian fluid.To extend the application of POD LDM to the aspect of heat convection for different types of fluids,we chose the typical physical model of Rayleigh-Benard(RBC)convection and use the Newton fluid and viscoelastic fluid individually to developing the corresponding LDM and further studied the ‘closure scheme' in different conditions.the main content are as follows:In chapter 1,we introduced the background and significance of POD low dimension model.In chapter 2,we shown the basic mathematical theory of POD analysis and the developing of low dimension model.At the end of this chapter,several schemes for modify the LDM are displayed.In chapter 3,we introduced the numerical method of DNS for Newton fluid and viscoelastic fluid individually,including the geometry size of RBC system,boundary condition,resolution and discrete method.Based on the calculation result of velocity field and temperature field,we shown the flow characters and heat transfer mechanism for the flow process.In chapter 4,we firstly calculated the POD basis using the DNS database and further established the LDM for Newtonian fluid.We found as the number of POD modes containing in the LDM increase,its accuracy also improves,however,the calculation time also adds a lot.to further reduce the calculation time and keep a high level of accuracy at the same time,we used the so called ‘eddy viscosity hypothesis' to modify the low dimension model,by comparing the calculation results with those of DNS,the accuracy of modified LDM obviously improves.Finally,we used the modified LDM to predict the unknow flow case of RBC convection,the calculation results show the modified LDM can be used for the process control of heat convection problems.In chapter 5,we shown the POD analysis for viscoelastic fluid and further developing the low dimension model.We also studied the accuracy of LDM with different number of POD modes and found the LDM of viscoelastic fluid also needs be corrected,we applied the so called ‘inner stabilization scheme' to correct the evolution of LDM,the calculation results shown the modified LDM coincide with DNS results well.